Showing papers by "John R. Birge published in 2003"
TL;DR: In this paper, a multistage stochastic programming model was developed for power system expansion under uncertainty, in which some of the variables are restricted to integer values, and an L-shaped algorithm was proposed to solve the problem.
Abstract: This paper is concerned with power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. We propose an L-shaped algorithm to solve the problem.
36 citations
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TL;DR: In this paper, the authors consider non-sealed bid online auctions of common products with quantity uncertainty and derive Nash equilibrium solutions, i.e., bidders' optimal bidding strategies, and the resulting market clearing prices.
Abstract: We consider non-sealed bid online auctions of common products with quantity uncertainty. Both first-price (also known as pay-as-you-bid) and uniform-price auctions are considered. In these auctions, all bidders have the same valuation of the products but may have different demand quantities. The number of units being auctioned can be random with a known and common distribution. Each bidder decides on a bidding price to maximize her profit. We derive Nash equilibrium solutions, i.e., bidders' optimal bidding strategies, and the resulting market clearing prices.
1 citations